diff --git a/src/body/incoming.rs b/src/body/incoming.rs
index 64ee5001a9..e85dceba42 100644
--- a/src/body/incoming.rs
+++ b/src/body/incoming.rs
@@ -270,7 +270,16 @@ impl Body for Incoming {
                         ping.record_non_data();
                         Poll::Ready(Ok(t.map(Frame::trailers)).transpose())
                     }
-                    Err(e) => Poll::Ready(Some(Err(crate::Error::new_h2(e)))),
+                    Err(e) => {
+                        match e.reason() {
+                            // These reasons should cause reading the trailers to stop, but not fail it.
+                            // The same logic as for `Read for H2Upgraded` is applied here.
+                            Some(h2::Reason::NO_ERROR) | Some(h2::Reason::CANCEL) => {
+                                Poll::Ready(None)
+                            }
+                            _ => Poll::Ready(Some(Err(crate::Error::new_h2(e)))),
+                        }
+                    }
                 }
             }
 
diff --git a/tests/client.rs b/tests/client.rs
index d5a0e4e005..b14c1008a0 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -2552,7 +2552,7 @@ mod conn {
     }
 
     #[tokio::test]
-    async fn http2_responds_before_consuming_request_body() {
+    async fn http2_responds_before_consuming_request_body_no_trailers() {
         // Test that a early-response from server works correctly (request body wasn't fully consumed).
         // https://github.com/hyperium/hyper/issues/2872
         use hyper::service::service_fn;
@@ -2596,15 +2596,96 @@ mod conn {
         let resp = client.send_request(req).await.expect("send_request");
         assert!(resp.status().is_success());
 
-        let mut body = String::new();
-        concat(resp.into_body())
+        let (body, trailers) = crate::concat_with_trailers(resp.into_body()).await.unwrap();
+        assert_eq!(body.as_ref(), b"No bread for you!");
+        assert!(trailers.is_none());
+    }
+
+    #[tokio::test]
+    async fn http2_responds_before_consuming_request_body_with_trailers() {
+        // Test that a early-response from server works correctly (request body wasn't fully consumed).
+        // https://github.com/hyperium/hyper/issues/2872
+        use hyper::body::{Body, Frame, SizeHint};
+        use hyper::header::{HeaderMap, HeaderValue};
+        use hyper::service::service_fn;
+
+        let _ = pretty_env_logger::try_init();
+
+        let (listener, addr) = setup_tk_test_server().await;
+
+        /// An `HttpBody` implementation whose `is_end_stream()` will
+        /// return `true` after sending trailers.
+        pub struct TrailersBody(Option<HeaderMap>);
+
+        impl Body for TrailersBody {
+            type Data = bytes::Bytes;
+            type Error = hyper::Error;
+
+            fn poll_frame(
+                mut self: Pin<&mut Self>,
+                _cx: &mut Context<'_>,
+            ) -> Poll<Option<Result<Frame<Self::Data>, Self::Error>>> {
+                if let Some(trailers) = self.0.take() {
+                    Poll::Ready(Some(Ok(Frame::trailers(trailers))))
+                } else {
+                    Poll::Ready(None)
+                }
+            }
+
+            fn is_end_stream(&self) -> bool {
+                self.0.is_none()
+            }
+
+            fn size_hint(&self) -> SizeHint {
+                SizeHint::with_exact(0)
+            }
+        }
+
+        // Spawn an HTTP2 server that responds before reading the whole request body.
+        // It's normal case to decline the request due to headers or size of the body.
+        tokio::spawn(async move {
+            let sock = TokioIo::new(listener.accept().await.unwrap().0);
+            hyper::server::conn::http2::Builder::new(TokioExecutor)
+                .timer(TokioTimer)
+                .serve_connection(
+                    sock,
+                    service_fn(|_req| async move {
+                        let mut trailers = HeaderMap::new();
+                        trailers.insert("grpc", HeaderValue::from_static("0"));
+                        let body = TrailersBody(Some(trailers));
+                        Ok::<_, hyper::Error>(http::Response::new(body))
+                    }),
+                )
+                .await
+                .expect("serve_connection");
+        });
+
+        let io = tcp_connect(&addr).await.expect("tcp connect");
+        let (mut client, conn) = conn::http2::Builder::new(TokioExecutor)
+            .timer(TokioTimer)
+            .handshake(io)
             .await
-            .unwrap()
-            .reader()
-            .read_to_string(&mut body)
-            .unwrap();
+            .expect("http handshake");
+
+        tokio::spawn(async move {
+            conn.await.expect("client conn shouldn't error");
+        });
+
+        // Use a channel to keep request stream open
+        let (_tx, recv) = mpsc::channel::<Result<Frame<Bytes>, Box<dyn Error + Send + Sync>>>(0);
+        let req = Request::post("/a").body(StreamBody::new(recv)).unwrap();
+        let resp = client.send_request(req).await.expect("send_request");
+        assert!(resp.status().is_success());
+
+        let (body, trailers) = crate::concat_with_trailers(resp.into_body()).await.unwrap();
+
+        // No body:
+        assert!(body.is_empty());
 
-        assert_eq!(&body, "No bread for you!");
+        // Have our `grpc` trailer:
+        let trailers = trailers.expect("response has trailers");
+        assert_eq!(trailers.len(), 1);
+        assert_eq!(trailers.get("grpc").unwrap(), "0");
     }
 
     #[tokio::test]